Regarding won games and steam reviews of them.

If you got it for free you check the box that tells you got it for free, simple.

You only need to use that if you received the game from the game publisher/developer for the purpose of writing the review. I believe this is because some laws were passed requiring it. Do a search online for "FTC review product" and you will find articles about it.

https://www.ftc.gov/tips-advice/business-center/guidance/ftcs-endorsement-guides-what-people-are-asking

I’m a blogger. I heard that every time I mention a product on my blog, I have to say whether I got it for free or paid for it myself. Is that true?

No. If you mention a product you paid for yourself, there isn’t an issue. Nor is it an issue if you get the product for free because a store is giving out free samples to its customers.

The FTC is only concerned about endorsements that are made on behalf of a sponsoring advertiser. For example, an endorsement would be covered by the FTC Act if an advertiser – or someone working for an advertiser – pays you or gives you something of value to mention a product. If you receive free products or other perks with the expectation that you’ll promote or discuss the advertiser’s products in your blog, you’re covered. Bloggers who are part of network marketing programs where they sign up to receive free product samples in exchange for writing about them also are covered.

No, why would I? It's not an actual review copy sent by the dev/publisher. That checkbox is phrased horribly, but it is meant to be used in those cases.

For me,a better question would be: "Do you write a more positive review for a game that was gifted to you by someone else, even if normally you would give it a thumbs down?"

no, i paid with points

I would only use it if I got the game from the developer.

Nope. I would only check it if the developers gave the key to me.

It's not received for free, someone else paid for it.

I dont mark the box, but I will mention I won the game in the review. I dont think it has any bearing other than sometimes Im reviewing a game in a genre I dont enjoy to begin with. So I offer it as a sort of explanation

Games we win here, aren't really "free", someone else paid for them, either by buying them, or by buying a bundle containing them.

Games gotten from developer sponsored giveaways, here, on Indie Gala, gleam.io, or woobox, are indeed to consider "free",
although the "product received for free" box isn't made for them either.

It's for keys sent for review purposes, so that we can judge whether a review marked that way is reliable or not.